87 lines
2.2 KiB
C
87 lines
2.2 KiB
C
|
/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */
|
||
|
|
/*
|
||
|
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||
|
|
* Debugged and optimized by Bruce D. Evans.
|
||
|
|
*/
|
||
|
|
/*
|
||
|
|
* ====================================================
|
||
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||
|
|
*
|
||
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||
|
|
* Permission to use, copy, modify, and distribute this
|
||
|
|
* software is freely granted, provided that this notice
|
||
|
|
* is preserved.
|
||
|
|
* ====================================================
|
||
|
|
*/
|
||
|
|
/* __rem_pio2f(x,y)
|
||
|
|
*
|
||
|
|
* return the remainder of x rem pi/2 in *y
|
||
|
|
* use double precision for everything except passing x
|
||
|
|
* use __rem_pio2_large() for large x
|
||
|
|
*/
|
||
|
|
|
||
|
|
#include "libm.h"
|
||
|
|
|
||
|
|
#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
|
||
|
|
#define EPS DBL_EPSILON
|
||
|
|
#elif FLT_EVAL_METHOD==2
|
||
|
|
#define EPS LDBL_EPSILON
|
||
|
|
#endif
|
||
|
|
|
||
|
|
/*
|
||
|
|
* invpio2: 53 bits of 2/pi
|
||
|
|
* pio2_1: first 25 bits of pi/2
|
||
|
|
* pio2_1t: pi/2 - pio2_1
|
||
|
|
*/
|
||
|
|
static const double
|
||
|
|
toint = 1.5/EPS,
|
||
|
|
pio4 = 0x1.921fb6p-1,
|
||
|
|
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||
|
|
pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
|
||
|
|
pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
|
||
|
|
|
||
|
|
int __rem_pio2f(float x, double *y)
|
||
|
|
{
|
||
|
|
union {float f; uint32_t i;} u = {x};
|
||
|
|
double tx[1],ty[1];
|
||
|
|
double_t fn;
|
||
|
|
uint32_t ix;
|
||
|
|
int n, sign, e0;
|
||
|
|
|
||
|
|
ix = u.i & 0x7fffffff;
|
||
|
|
/* 25+53 bit pi is good enough for medium size */
|
||
|
|
if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */
|
||
|
|
/* Use a specialized rint() to get fn. */
|
||
|
|
fn = (double_t)x*invpio2 + toint - toint;
|
||
|
|
n = (int32_t)fn;
|
||
|
|
*y = x - fn*pio2_1 - fn*pio2_1t;
|
||
|
|
/* Matters with directed rounding. */
|
||
|
|
if (predict_false(*y < -pio4)) {
|
||
|
|
n--;
|
||
|
|
fn--;
|
||
|
|
*y = x - fn*pio2_1 - fn*pio2_1t;
|
||
|
|
} else if (predict_false(*y > pio4)) {
|
||
|
|
n++;
|
||
|
|
fn++;
|
||
|
|
*y = x - fn*pio2_1 - fn*pio2_1t;
|
||
|
|
}
|
||
|
|
return n;
|
||
|
|
}
|
||
|
|
if(ix>=0x7f800000) { /* x is inf or NaN */
|
||
|
|
*y = x-x;
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
/* scale x into [2^23, 2^24-1] */
|
||
|
|
sign = u.i>>31;
|
||
|
|
e0 = (ix>>23) - (0x7f+23); /* e0 = ilogb(|x|)-23, positive */
|
||
|
|
u.i = ix - (e0<<23);
|
||
|
|
tx[0] = u.f;
|
||
|
|
n = __rem_pio2_large(tx,ty,e0,1,0);
|
||
|
|
if (sign) {
|
||
|
|
*y = -ty[0];
|
||
|
|
return -n;
|
||
|
|
}
|
||
|
|
*y = ty[0];
|
||
|
|
return n;
|
||
|
|
}
|